Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

Online
ISSN
1615-7168
See all formats and pricing
More options …
Volume 17, Issue 1

Issues

The automorphism groups of doubly transitive bilinear dual hyperovals

Ulrich Dempwolff
  • Corresponding author
  • Department of Mathematics, University of Kaiserslautern, Erwin-Schroedinger-Strasse, 67653 Kaiserslautern, Germany
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-02-16 | DOI: https://doi.org/10.1515/advgeom-2016-0030

Abstract

We determine the automorphism groups of the 2-transitive, bilinear dual hyperovals over 𝔽2 of type D[k] constructed in [6] by the author. Then we characterize the 2-transitive quotients of the Huybrechts dual hyperovals, compute their automorphism groups and give estimates on the number of such quotients.

Keywords: Dual hyperoval; Huybrechts dual hyperoval; automorphism group

Communicated by: W. M. Kantor

References

  • [1]

    M. Aschbacher, Finite group theory. Cambridge Univ. Press 2000. MR1777008 (2001c:2000l) Zbl 0997.20001Google Scholar

  • [2]

    G. W. Bell, On the cohomology of the finite special linear groups. I, II. J. Algebra 54 (1978), 216–238, 239–259. MR511463 (80i:20025) Zbl 0389.20043Google Scholar

  • [3]

    J.N. Bray, D.F.Holt,C.M. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups. Cambridge Univ. Press 2013. MR3098485 Zbl 1303.20053Google Scholar

  • [4]

    P. Cameron, Finite permutation groups and finite simple groups. Bull. London Math. Soc.13 (1981),1–22. MR599634 Zbl 0463.20003Google Scholar

  • [5]

    U. Dempwolff, Automorphisms and equivalence of bent functions and of difference sets in elementary abelian 2-groups. Comm. Algebra 34 (2006), 1077–1131. MR2208119 (2006m:05035) Zbl 1085.05019Google Scholar

  • [6]

    U. Dempwolff, Some doubly transitive bilinear dual hyperovals and their ambient spaces. European J. Combin. 44 (2015), 1–22. MR3278768 Zbl 1341.51008Google Scholar

  • [7]

    U. Dempwolff, Universal covers of dimensional dual hyperovals. Discrete Math. 338 (2015), 633–636. MR3300751 Zbl 1320.51010Google Scholar

  • [8]

    U. Dempwolff, Y. Edel, Dimensional dual hyperovals and APN functions with translation groups. J. Algebraic Combin. 39 (2014), 457–496. MR3159259 Zbl 1292.05068Google Scholar

  • [9]

    The GAP-group, Groups Algorithms and Programming with translation groups.Version 4.4, 2004. http://www.gap-system.org

  • [10]

    R. L. Griess, Jr., On a subgroup of order 2151 GL(5, 2)| in E8(𝕔), the Dempwolff group and Aut(D8D8D8). J. Algebra 40 (1976), 271–279. MR0407149 (53 #10932) Zbl 0348.20011Google Scholar

  • [11]

    T. Grundhöfer, P. Müller, Sharply 2-transitive sets of permutations and groups of affine projectivities. Beiträge Algebra Geom. 50 (2009), 143–154. MR2499785 (2010a:20005) Zbl 1165.20002Google Scholar

  • [12]

    R. Guralnick, T. Penttila, C. E. Praeger, J. Saxl, Linear groups with orders having certain large prime divisors. Proc. London Math. Soc. (3) 78 (1999), 167–214. MR1658168 (99m:20113) Zbl 1041.20035Google Scholar

  • [13]

    B. Huppert, N. Blackburn, Finite groups. //. Springer 1982. MR650245 (84i:20001a)Zbl 0477.20001Google Scholar

  • [14]

    C. Huybrechts, Dimensional dual hyperovals in projective spaces and c · AG*-geometries. Discrete Math. 255 (2002), 193–223. MR1927795 (2003i:51004) Zbl 1024.51010Google Scholar

  • [15]

    W. M. Kantor, Linear groups containing a Singer cycle. J. Algebra 62 (1980), 232–234. MR561126 (81g:20089) Zbl 0429.20004Google Scholar

  • [16]

    P. Kleidman, M. Liebeck, The subgroup structure of the finite classical groups. Cambridge Univ. Press 1990. MR1057341 (91g:20001) Zbl 0697.20004Google Scholar

  • [17]

    M. W. Liebeck, The affine permutation groups of rank three. Proc. London Math. Soc. (3) 54 (1987), 477–516. MR879395 (88m:20004) Zbl 0621.20001Google Scholar

  • [18]

    C.M.Roney-Dougal,The primitive permutation groups of degree less than 2500. J. Algebra 292 (2005),154–183. MR2166801 (2006e:20005) Zbl 1107.20001Google Scholar

  • [19]

    L. Schneider, Minimale Darstellungen endlicher klassischer Gruppen in natürlicher Charakteristik. Cuvillier Verlag, 2004.Google Scholar

  • [20]

    H. Taniguchi, New dimensional dual hyperovals, which are not quotients of the classical dual hyperovals. Discrete Math. 337 (2014), 65–75. MR3262362 Zbl 1303.51003Google Scholar

  • [21]

    S. Yoshiara, Ambient spaces of dimensional dual arcs. J. Algebraic Combin.19 (2004), 5–23. MR2056764 (2005c:51013) Zbl 1086.51009Google Scholar

  • [22]

    S. Yoshiara, Dimensional dual arcs–a survey. In: Finite geometries, groups, and computation, 247–266,de Gruyter 2006. MR2258014 (2007e:51010) Zbl 1100.51006Google Scholar

  • [23]

    S. Yoshiara, Dimensional dual hyperovals with doubly transitive automorphism groups. European J. Combin. 30 (2009), 747–757. MR2494448 (2009m:51017) Zbl1166.51005Google Scholar

  • [24]

    K. Zsigmondy, Zur Theorie der Potenzreste. Monatsh. Math. Phys. 3 (1892), 265–284. MR1546236 JFM 24.0176.02Google Scholar

About the article

Received: 2015-03-20

Published Online: 2017-02-16

Published in Print: 2017-01-01


Citation Information: Advances in Geometry, Volume 17, Issue 1, Pages 91–108, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2016-0030.

Export Citation

© 2017 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Ulrich Dempwolff
Journal of Algebraic Combinatorics, 2019

Comments (0)

Please log in or register to comment.
Log in